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The differential equation dx/dt = (1 - x)/τ is discretised using Euler’s numerical integration method with a time step ΔT > 0. What is the maximum permissible value of ΔT to ensure stability of the solution of the corresponding discrete time equation?

1. 1
2. τ/2
3. τ
4. 2τ

Correct answer: 2τ

Solution

The stability of the discretized equation using Euler's method requires that the time step ΔT be less than or equal to 2τ. This ensures that the numerical solution does not diverge and remains stable, as larger time steps can lead to oscillations or instability in the solution.

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